Macrocausality
Macrocausality is a term coined to describe the assumption made by Anthony James Leggett and Anupam Garg in their development of a 'temporal Bell Inequality' to test quantum casuality. The Leggett-Garg test effectively forces a macrocausal system, i.e: 'a system that is presumed to have macroscopic explanations for all of its behaviour'within the limits imposed by quantum uncertainties in its behaviour, to behave in ways that it appears to statistically self-correlate in time. That is to say, it appears to align its unknown past behaviour with the measured state it obtains in the future. Leggett-Garg Test The experimenter spins an energetic quantum wheel (photons, electrons, protons, or any other multi-level quantum system {MLQS}) and measures its phase at three different times. By releasing the wheel at the peak (or trough) of its phase evolution the experimenter sets the state, S, =0 for time, t, =0 seconds. Then, the experimenter waits either '''for T seconds and then measures, '''or after T seconds, does nothing and instead waits a total of 2T seconds before measuring the final state of the wheel. Depending on the speed of the wheel, the relative difference between these two measurements can be tuned. For example, if the period of the wheel is 2T then it will return to S=0 with certainty for the second measurement, while at time t=T it will be in a state S=1 with (approximate) certainty, hence this frequency leads to maximum disagreement between these two measurements. Conversely, if the period of the wheel is T, then both times will correspond to S=0 and hence this leads to minimum disagreement between the measurements and the three times t=0,T,2T all produce states of S=0. Tuning the speed (or the time, T) such that the phase traveled by the wheel at time t=T is '2π/3' (120'°') leads to a state that is 75% likely to give S=1 and 25% likely to give S=0. With this same speed, the wheel will rotate another 120° by time t=2T and end up with 240° phase in total. However, since 120° and 240° are both closer to 180° than 0° and both within 60° of 180°, they have the same probabilities: 75% likely to give S=1 and 25% likely to give S=0. (will finish later, hard to navigate here because assuming only two measurements is akin to the stationarity assumption of Knee et. al., and this will take extra explanation if done this way) ... Effectively, choosing this wheel speed leads the experiment into a position where the experimenter ''if they believe in macrocausality as the true reality of the state, will be in a position to say that: - At time t=T, the wheel would most likely (75% of the time) be measured as S=1 if I made a measurement, implying 180°. - Therefore, if I rotate it another 120°, then 75% of the time this should imply it sits at 300° which implies a 75% chance of landing on S=0. Whereas for the 25% of the time that I would have measured 0°, then it will behave as if it's only at 120° and the chances of S=1 will be 75% instead. - Taking these paths out, implies that the odds of S=0 become 0.75*0.75=9/12, while the odds of S=1 become 0.25*0.75=3/12. Splitting the experiment up into macrocausal states that were never measured but '''could have been', and then using the known statistics they would have taken, then implies that the final measurement will favour S=0, even though the quantum calculations suggest S=1 will be favoured. All of this hinges on the counterfactual logic that an experimenter can make conclusions about what would have happened to set predictions about what will happen after choosing to not make a measurement. When actually tested, the results indeed follow the standard quantum statistics, indicating that counterfactual reasoning fails here, just as in Quantum Bell Experiments. Macrorealism The actual assumption used by Leggett was referred to as 'macroscopic realism' and later 'macrorealism' or 'macrorealism per se'. However, Leggett later conceded an implicit assumption referred to as 'induction' which was essentially a 'no retrocausality' clause, hence here we coin 'macrocausality' as an all-encompassing term.Category:Quantum Category:Physics Category:Materialism Category:Leggett-Garg Category:Quantum Entanglement Category:Quantum Philosophy